Question

Write 2.3181818... as a mixed number.

Answer 1

Answer:

x =  $\frac{51}{22}$.

Step-by-step explanation:

Given  :  2.3181818...

To find : write as a mixed number.

Solution : We have given that

2.3181818...

Let x = 2.3181818...

We can see the number 18 is repeating 18181818......

So, the bar line is over the two digit 18

$x = 2.318.....$.

On multiplying the number both side by 100.

$100x = 100 * 2.318.....$.

100x = 231.81818.....

We can write the number 231.81818..... in term of x

100x = 229 .5 + x

On subtracting both sides by x

100x -x = 229.5

99x = 229.5

On dividing both sides by 99.

x = $\frac{229.5}{99}$.

x =  $\frac{2295}{990}$.

x =  $\frac{459}{198}$.

x =  $\frac{51}{22}$.

Therefore, x =  $\frac{51}{22}$.

Answer 2

Assuming the pattern continues, let $x=2.3181818\ldots=2.3\overline{18}$.

Then $10x=23.\overline{18}$ and $1000x=2318.\overline{18}$, and we have

$1000x-10x=990x=2295\implies x=\dfrac{2295}{990}=\dfrac{51}{22}$

Since $51=2\cdot22+7$, we can write $x$ as the mixed number $2+\dfrac7{22}$.